Excitonic Splitting and Vibronic Coupling Analysis of the m

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Excitonic Splitting and Vibronic Coupling Analysis of the Meta-Cyanophenol Dimer Franziska A Balmer, Sabine Kopec, Horst Koeppel, and Samuel Leutwyler J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.6b10416 • Publication Date (Web): 06 Dec 2016 Downloaded from http://pubs.acs.org on December 10, 2016

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The Journal of Physical Chemistry

Excitonic Splitting and Vibronic Coupling Analysis of the meta-Cyanophenol Dimer Franziska A. Balmer,† Sabine Kopec,‡ Horst Köppel,‡ and Samuel Leutwyler∗,† Department of Chemistry and Biochemistry, University of Bern, Freiestrasse 3, CH-3012 Bern, Switzerland, and Theoretische Chemie, Physikalisch-Chemisches Institut, Universität Heidelberg, Im Neuenheimer Feld 229, D-69120 Heidelberg, Germany. E-mail: [email protected]

Abstract The S1 /S2 splitting of the meta-cyanophenol dimer, (mCP)2 , and the delocalization of its excitonically coupled S1 /S2 states are investigated by mass-selective two-color resonant two-photon ionization and dispersed fluorescence spectroscopy, complemented by a theoretical vibronic coupling analysis based on correlated ab initio calculations at the approximate coupled cluster CC2 and SCS-CC2 levels. The calculations predict three close-lying groundstate minima of (mCP)2 : The lowest is slightly Z-shaped (Ci -symmetric), the second-lowest is < 5 cm−1 higher and planar (C2h ). The vibrational ground state is probably delocalized over both minima. The S0 → S1 transition of (mCP)2 is electric-dipole allowed (Ag → Au ), while the S0 → S2 transition is forbidden (Ag → Ag ). Breaking the inversion symmetry by 12 C/13 C- or H/D-substitution renders the S0 → S2 transition partially allowed; the excitonic contribution to the S1 /S2 splitting is ∆exc = 7.3 cm−1 . Additional isotope-dependent contributions arise from ∗ To

whom correspondence should be addressed of Chemistry and Biochemistry, University of Bern, Freiestrasse 3, CH-3012 Bern, Switzerland ‡ Theoretische Chemie, Physikalisch-Chemisches Institut, Universität Heidelberg, Im Neuenheimer Feld 229, D69120 Heidelberg, Germany. † Department

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the changes of the m-cyanophenol zero-point vibrational energy upon electronic excitation, which are ∆iso (12 C/13 C) = 3.3 cm−1 and ∆iso (H/D) = 6.8 cm−1 . Only partial localization of the exciton occurs in the 12 C/13 C and H/D substituted heterodimers. The SCS-CC2 calculated excitonic splitting is ∆el = 179 cm−1 ; when multiplying this with the vibronic quenching facexp −1 tor Γexp vibron = 0.043, we obtain an exciton splitting ∆vibron = 7.7 cm , which agrees very well

with the experimental ∆exc = 7.3 cm−1 . The semiclassical exciton hopping times range from 3.2 ps in (mCP)2 to 5.7 ps in the heterodimer (mCP-h)·(mCP-d). A multimode vibronic coupling analysis is performed encompassing all the vibronic levels of the coupled S1 /S2 states from the v=0 level to 600 cm−1 above. Both linear and quadratic vibronic coupling schemes were investigated to simulate the S0 → S1 /S2 vibronic spectra, those calculated with the latter scheme agree better with experiment.

1 Introduction Excitonic interactions between chromophores play an important role for electronic energy transfer in a wide range of photochemical and biological systems such as conjugated polymers, molecular crystals and photosynthetic light-harvesting complexes. 1–8 Gas-phase hydrogen-bonded molecular dimers can be used to investigate these interactions since they are representative of larger systems, but are still small enough to yield well-resolved vibronic spectra and allow high-level ab initio calculations and vibronic coupling treatments. We have been studying the excitonic S0 → S1 /S2 splittings in rigid, doubly H-bonded aromatic dimers such as (2-pyridone)2 , (2-aminopyridine)2 , (benzoic acid)2 , (benzonitrile)2 and (ortho-cyanophenol)2 by mass- and isotope-selective two-color resonant two-photon ionization (2C-R2PI) spectroscopy with vibronic coupling calculations. 9–18 These dimers are all inversion-symmetric, which implies that the S1 excited states of their constituent monomers A and B are degenerate at large intermolecular distance. When the doubly H-bonded dimer is formed, the intermolecular coupling splits the monomer states into two nondegenerate excitonic states, one of which is symmetric (g) and the other antisymmetric (u), rendering the S0 → S1 /S2 electronic transitions forbidden and allowed, respectively. Isotopic substitution 2 ACS Paragon Plus Environment

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breaks the inversion symmetry of the dimer sufficiently to render the forbidden excitonic transition allowed, enabling to experimentally determine the S1 ↔ S2 excitonic splitting. 9–18 We have previously shown that the coupling of the S1 and S2 states to excited-state intra- and intermolecular vibrations has a substantial impact on the magnitude of the excitonic energy splittings. 13,16 The observed splittings are up to 40 times smaller than the electronic Davydov splittings that are predicted by ab initio calculations. 9–18 This so-called “vibronic quenching” of the electronic excitonic splitting can be explained by taking the vibrational normal modes into account within Förster’s perturbation theory approach 19 and the Fulton-Gouterman model. 20,21 Applying the vibronic quenching factor Γvibron to the calculated Davydov splitting resulted in vibronic splittings very close to the experimentally observed S1 /S2 splittings. 13,15,17 Here, we combine experimental spectroscopic investigations, ab initio calculations and vibroniccoupling theory treatments to explain the S1 /S2 state excitonic splitting and vibronic band structure of the meta-cyanophenol dimer, (mCP)2 . In contrast to the previously studied doubly H-bonded dimers, 9–18 the S0 → S1 transition of (mCP)2 is fully allowed, while the S0 → S2 transition is forbidden. This is due to the orientation of the mCP monomer electronic transition dipole moments, relative to the inter-monomer vector RAB between the centers of mass of A and B, see Figure 1. Zehnacker and co-workers have previously studied mCP and (mCP)2 by laser-induced fluorescence and fluorescence dip-IR spectroscopy. 22 They observed both the cis- and trans-mCP rotamers, whose OH groups are oriented towards and away from the CN group. They reported that the meta-cyanophenol dimer, (mCP)2 , is dominantly formed by the cis-mCP rotamer, which can form two antiparallel OH· · · N hydrogen bonds, while the trans-mCP dimer, which can only form a single H-bond, was not observed experimentally. 22 They proposed vibronic assignments of the observed bands and identified several fundamental transitions of non-totally-symmetric vibrations. In Ci -symmetry, these transitions would not be allowed. Hence, Zehnacker and co-workers concluded a loss of symmetry upon excitation that renders the fundamental transitions of non-totally symmetric vibrations allowed; the loss of symmetry was thought to cause a localization of the electronic excitation on one of the monomers. 22



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Below, we present the mass-selected two-color resonant two-photon ionization spectra of the homodimers (mCP)2 and (mCP-d)2 , and of the singly isotopically substituted (mCP)·(mCP-13 C) and (mCP-h)·(mCP-d) heterodimers. From the latter two spectra we determine the S1 /S2 splittings and the contribution of the

12 C/13 C

and H/D isotopic mass changes on the splitting, similar to

(benzoic acid)2 and (benzonitrile)2 . 14,15 A computational investigation of the (mCP)2 ground state using correlated ab initio methods reveals four different minimum-energy structures. The normal modes of the two lowest-energy structures form the basis for the following vibronic coupling treatment and band assignments in the spectrum of (mCP)2 . The linear and quadratic vibronic coupling schemes are employed 23 to simulate the theoretical vibronic spectra. The influence of the vibronic coupling on the excitonic energy splitting is discussed and the question of the localization of the excited states addressed. While the S1 /S2 coupled states are completely delocalized in the (mCP)2 and (mCP-d)2 homodimers, asymmetric isotopic substitution partially localizes the two electronic transitions. Using the effective-mode approximation introduced by Köppel and co-workers, 24 we show that the double-minimum character of the lower excited state of the homodimer does not imply a localization of the excitation as proposed by Zehnacker and co-workers. 22

2 Theoretical Framework for Multimode Vibronic Coupling Recently, Köppel and co-workers have extended the analysis from the S1 /S2 splitting to simulating the six-dimensional vibronically coupled spectra of (o-cyanophenol)2 and (2-pyridone)2 , and compared them to the 2C-R2PI spectra. 16,18 The representation of the vibronic coupling in the framework of the Fulton-Gouterman model 20,21 was seen to be insufficient. Instead they adopted the more general linear and quadratic vibronic coupling schemes. 16,18,23 These naturally include certain important intermolecular normal modes in the analysis, resulting in convincing simulations of the S0 → S1 /S2 vibronic spectra that were in good agreement with experiment. 16,18 Other extensions of the Fulton-Gouterman model to vibronic coupling in excitonic systems have been made, see, for example, the application to bichromophores by Slipchenko, Zwier and co-workers. 25–27


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2.1 The Multimode Vibronic Coupling Model The S0 → S1 /S2 vibronic spectrum of (mCP)2 is investigated by means of the multimode vibronic coupling model described in ref. 23, including 12 vibrational modes, of which seven are totallysymmetric (ag ) and five are non-totally symmetric (au ). This model has been applied before to (ortho-cyanophenol)2 and (2-pyridone)2 , and is there explained in detail. 16,18 The Hamiltonian is constructed in a diabatic basis with a diagonal nuclear kinetic energy operator TN and a coupling matrix W emerging from the potential energy part.

H = TN 1 + W(Q)

(1)

The coupling matrix elements are smooth functions of the dimensionless normal mode coordinates Qi , and are expanded in a Taylor series around the ground-state equilibrium geometry Q0 = 0. To obtain the linear (LVC) and quadratic (QVC) vibronic coupling models, the Taylorseries is truncated after the first and second order term, respectively. 18,23 Coupling constants are the building blocks of the coupling matrix and are restricted by symmetry selection rules, determining which vibrational normal modes are relevant in the diagonal and off-diagonal elements. Vibrational modes with irreducible representation ΓQ can couple electronic states 1 and 2 with corresponding irreducible representations Γ1 and Γ2 only if their direct product comprises the totally symmetric representation ΓAg . Γ1 ⊗ ΓQ ⊗ Γ2 ⊃ ΓA g .

(2)

In the linear vibronic coupling model, the totally symmetric normal modes (index g) lead to intrastate coupling, while non-totally symmetric normal modes (index u) lead to interstate coupling, if their symmetry is compatible with Equation 2 (in the point group of interest). (mCP)2 is Ci symmetric (see below), hence, only ag and au vibrations exist. The symmetries of the two excited electronic states of interest are Ag and Au , thus all modes are relevant for the coupling matrix. A



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double-well structure of the lower electronic state along the respective normal mode coordinate Qu arises if the interstate coupling constants are sufficiently large. The totally symmetric modes (tuning modes) affect the energy separation between the coupled electronic states. 23 The multimode linear vibronic coupling Hamiltonian comprising two electronic states is defined as: 23   (1) ∑ j λ j Qu j  E1 + ∑i κi Qgi W(1) (Qg , Qu ) = ∑ V0 (Qgi , Qu j )1 +  , (2) i, j E2 + ∑i κi Qgi ∑ j λ j Qu j where the ground state potential is given as V0 (Qgi , Qu j ) =

h¯ ωu j 2 h¯ ωgi 2 2 Qgi + 2 Qu j .

(3)

E1,2 are the elec-

tronic excitation energies of the respective state, κ is the intrastate vibronic coupling constant and

λ the interstate vibronic coupling constant. To include quadratic coupling terms, the Hamiltonian is extended. For reasons of simplicity, it is shown for a two-state/two-mode system including one tuning mode Qg and one coupling mode Qu : W(2) (Qg , Qu ) =V0 (Qg , Qu )1+   (1) (1) 1 1 1 2 2 (1) λ Qu + 2 µgu Qg Qu E1 + κ Qg + 2 γg Qg + 2 γu Qu    (2) (2) 1 1 1 (2) 2 2 λ Qu + 2 µgu Qg Qu E2 + κ Qg + 2 γg Qg + 2 γu Qu

(4)

The quadratic coupling constant γ accounts for frequency changes upon excitation. The mixed quadratic coupling µgu needs to be considered when analyzing multidimensional cuts through the potential energy surfaces (PESs). Here, we are only considering one-dimensional cuts and µgu is put to zero. Quite generally, all 2nd-order coupling terms off-diagonal in the vibrational modes (“Dushinsky mixing”) are suppressed in the Hamiltonian. This is motivated by ample positive experience with the LVC model Hamiltonian which is already extended by the present approach (namely, including diagonal second-order coupling terms). The adiabatic PES along the normal mode coordinates Qg and Qu are obtained by diagonaliza-


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tion of the diabatic coupling matrix W and result in the following expressions: 23 (1,2)

h¯ ωg 2 γg Q + Q2g + κ (1,2) Qg + E1,2 2 g 2 (1) (2) h¯ ωu 2 E1 + E2 γu + γu V1,2 (Qu ) = Q + + Q2u 2v u 2 4 )2 u( (2) (1) u E −E γu − γu 2 1 t ± + Q2u + (λ Qu )2 2 4

V1,2 (Qg ) =

(5)

(6)

From these PESs, the intrastate coupling constant κ and the quadratic coupling constant γ can be derived as follows:

κ (i) =

∂ Vi (Q) |Q=0 ∂ Qg

(i = 1, 2)

(i)

γg =

∂ 2Vi (Q) |Q=0 ∂ Q2g

(i = 1, 2; for ωg = 0)

(7)

The interstate coupling constant λ and the corresponding quadratic coupling constants γu are obtained from the sum and difference of the adiabatic PES, see below.

2.2 Dynamical Calculations The S0 → S1 /S2 vibronic spectra are simulated via wave-packet propagation with the multiconfigurational time-dependent Hartree (MCTDH) method. 28–30 The spectral intensity distribution P(E) is obtained by Fourier transformation of the autocorrelation function C(t). 29 P(E) ∝

∫

eiEt C(t)dt,

with C(t) = ⟨Ψ(0)|Ψ(t)⟩

(8)

C(t) is a measure for the probability that the wave function at a time t is equal to the initial wave function. MCTDH uses a multiconfigurational wave function, which is the weighted sum over Hartree products of optimized time-dependent basis functions ϕ , called single-particle functions,



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for every degree of freedom f . Ψ(Q1 , ..., Q f ,t) =

n1

∑

j1 =1

nf

···

∑ A j1··· j f (t)ϕ j1

(1)

j f =1

(f)

(Q1 ,t) · · · ϕ j f (Q f ,t)

(9)

Equations of motion for the expansion coefficients A j and the single-particle functions are derived through the Dirac-Frenkel variational principle.

3 Methods 3.1 Computational Methods The mCP dimer was optimized with the approximate coupled-cluster singles and doubles method (CC2), using the resolution-of-identity (RI) and its spin-component scaled variant (SCS-CC2), 31–33 and the aug-cc-pVDZ and aug-cc-pVTZ basis sets. Four minimum-energy structures were found, which are discussed below. Vertical excitation energies to the S1 and S2 state were calculated at the minima using the SCS-CC2 method. The spin-component-scaled variant of the CC2 method was applied because it has recently been found to yield highly reliable results for the valence excitations of aromatic molecules. 34 To calculate the vibronic lines in the S0 → S1 /S2 spectrum, the (mCP)2 ground state was optimized at the SCS-CC2/aVTZ level and normal-mode calculations were performed on this structure. One-dimensional cuts through the PESs were obtained by calculating the vertical SCS-CC2/aVTZ excitation energies at geometries that were displaced by Q = ±0.5, ±1, ±2, ±3 along the S0 state normal-mode eigenvectors. All calculations were carried out using the Turbomole V6.3 program package. 35,36 For the mCP monomer, the PES needed to determine the Huang-Rhys factors to evaluate the quenching factor Γ were calculated in the same manner as for the dimer, but with the SCS-CC2/cc-pVTZ method.


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3.2 Experimental Setup The mCP dimers are produced in a pulsed supersonic expansion of mCP (Aldrich, 99%) heated to 80 ◦ C, seeded in Ne carrier gas at p0 = 1.2 bar and expanded through a 20 Hz repetition rate pulsed nozzle (0.4 mm diameter). Mass-selective two-color resonant two-photon ionization (2C-R2PI) spectra were recorded by crossing the skimmed molecular beam with temporarily and spatially overlapping excitation and ionization laser beams in the source chamber of a time-of-flight mass spectrometer. For excitation, the frequency doubled output of a Nd:YAG-pumped Radiant Dyes NarrowScan dye laser (Sulforhodamine B in EtOH) with a bandwidth of 0.04 cm−1 was used. All spectra were vacuum-corrected. For the ionization step we used an Ekspla NT342B UV optical parametric oscillator/optical parametric amplifier (OPO/OPA) operated at 245 nm (1 mJ/pulse). The fluorescence emission spectra were measured by crossing the unskimmed molecular beam with the UV excitation laser beam, fixed at the mCP 000 band, about 4 mm downstream of the nozzle. The fluorescence emission was collected using a spherical mirror and quartz optics, dispersed in a SOPRA UHRS 1.5 m monochromator in second order and detected by a Peltier-cooled Hamamatsu R928 photomultiplier. The

13 C-isotopomer

spectra were measured using the natural

13 C

abundance of 15.5% for

(mCP)2 . Deuterated mCP was obtained by dissolving mCP in CD3 OD (99.8 atom-% D), refluxing for 3 hours, and evaporating the perdeuteromethanol, leading to ∼75% deuteration of the hydroxy group. The spectra of (mCP-h)(mCP-d) were recorded using mixtures of mCP-h and mCP-d.

4 Results 4.1 Equilibrium Geometries and Vibrational Analysis Figure 2 shows the three lowest-energy (mCP)2 structures, as optimized at the SCS-CC2/augcc-pVTZ level. The CC2 and SCS-CC2 calculated relative energies are listed in Table 1. A π stacked geometry was found at the CC2 and SCS-CC2/aug-cc-pVDZ levels, but is predicted to



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lie 270 − 470 cm−1 higher; its structure is shown in Figure S1 (Supporting Information). The Cartesian coordinates of the four structures in Table 1 are given in Tables S1 to S4. While both CC2 and SCS-CC2 predict that the Z-shaped Ci -symmetric and the C2h -symmetric planar structure are degenerate when using the aug-cc-pVDZ basis set, the SCS-CC2/aug-cc-pVTZ calculation yields minima differing by 0.1 cm−1 . With CC2/aVTZ the C2h structure is an index-1 saddle point 5.5 cm−1 above the Ci global minimum. All calculations predict a third “V-shaped” and C2 -symmetric structure 3 − 11 cm−1 above the global minimum. Zehnacker and co-workers optimized (mCP)2 at the B3LYP/6-31G** level, which also yielded a Ci -symmetric structure. 22 In Ci symmetry all calculations predict the planes of the mCP subunits to be displaced along the z-axis, see Figure 2. The calculated displacement distance is ∆z = ±0.12 Å with CC2 and ±0.03 Å with SCS-CC2, using the aug-cc-pVTZ basis set. Figure 2 also shows the low-frequency largeamplitude intermolecular vibrations that interconvert these structures. The C2h and two symmetryequivalent Ci minima are connected by the “stagger” vibration δ . The V-shaped C2 structure is interconverted to its enantiomer via the planar C2h structure by the β “bending” vibration. Given the tiny energy differences between the C2h and Ci minima, the barrier along the δ vibrational coordinate is probably so small that the lowest vibrational level is delocalized over all three minima. Below, we will consider the SCS-CC2/aVTZ results only.

4.2 S0 → S1 /S2 Electronic Transitions An important difference between (mCP)2 and the previously investigated H-bonded dimers 9–18 is that in (mCP)2 the S0 → S1 transition is 1 Ag →1 Bu and electric-dipole allowed, while the S0 → S2 transition is 1 Ag →1 Ag and dipole-forbidden. In the previously investigated dimers, the angle between the transition dipole moments (TDM) of the monomer moieties and the intermonomer vector RAB is larger than the "magic angle" θm = 54.7◦ for dipole↔dipole interactions, which is given by cos2 (θm ) = 1/3. The calculated TDM angles are θ = 85◦ in (2-pyridone)2 , 13 88◦ in (benzoic acid)2 , 13 59◦ in (ortho-cyanophenol)2 , 17 77◦ in (2-aminopyridine)2 , 17 and 63◦ in (benzonitrile)2 . 15 For (mCP)2 however, both the CC2 and SCS-CC2 calculations predict that θ = 11◦ , i.e., that the 10 ACS Paragon Plus Environment

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TDMs are nearly collinear, as shown in Figure 1. The relative intensities of the S0 → S1 and S0 → S2 transitions depend on the θ , as schematically depicted in Figure 3(a,b). As θ decreases, the TDM orientation changes from parallel/antiparallel, Figure 3(a), to collinear/anti-collinear in Figure 3(b). As shown to the left of Figure 3(a,b), the transition-dipole ↔ transition-dipole interaction splits the S1 and S2 states by the energy Vdd :

Vdd =

) |⃗µA ||⃗µB | ( · 2cos2 θ + sin2 θ · cosϕ 3 4πε0 RAB

(10)

where ϕ is zero if the two molecules are coplanar. The calculated vertical excitation energies are given in Table 2. All calculations agree that the S0 → S2 transition is forbidden in Ci and C2h symmetries, while it is weakly allowed in C2 . The CC2 and SCS-CC2 calculated vertical excitation energies of the Ci , C2h and C2 isomers change only by a few cm−1 between different method/basis set combination, see Table 2, and the purely electronic S1 /S2 splittings are between 173 and 201 cm−1 .

4.3 Dispersed Fluorescence Spectrum The dispersed fluorescence (DF) spectrum of (mCP)2 was measured by exciting at the S0 → S1 000 band (33255 cm−1 ) and is shown in Figure 4. Overall, the DF spectrum agrees well with that of Zehnacker and co-workers and many vibrational assignments are the same as those proposed in reference 22. However, we have changed the assignments of the δ ′′ , β ′′ , σ ′′ and χ ′′ intermolecular vibrations from those in reference 22 so that the agreement with the SCS-CC2/aVTZ harmonic frequencies is better. The frequencies and band assignments are listed in Table 3, together with the calculated S0 state and experimental S1 state frequencies.

4.4 Two-Color Resonant Two Photon Ionization Spectrum The two-color resonant two-photon ionization spectrum of (mCP)2 was recorded in the 33200 − 33850 cm−1 region and is shown in Figure 5. The S0 → S1 electronic origin is at 33255 cm−1 . Both 11 ACS Paragon Plus Environment


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the position of the origin and the vibronic band positions agree within ±1 cm−1 with those reported in ref. 22. The vibronic bands were assigned to based on the dispersed fluorescence spectrum (see Section 4.3)and on the calculated SCS-CC2/aVTZ frequencies. We have assigned the lowest-lying

δ ′ and β ′ as well as the χ ′ and σ ′ vibrations oppositely to those in ref. 22, all other assignments are the same, and are listed in Table 3. The fact that the δ ′′ vibrational fundamental, which transforms as ag in Ci is discernible in the DF and is clear in the R2PI spectrum strongly suggests that the S0 state structure is effectively Ci symmetric. As discussed in section 4.1, the v′′ = 1 and higher levels of the δ ′′ vibration may be delocalized over the C2h and both Ci structures. However, since the β vibration is non-totally symmetric (au ) in Ci symmetry it should not appear as a fundamental, as is indeed the case for the DF spectrum, where β01 does not appear but β02 is observed. In the R2PI spectrum, we observe a weak band at 000 + 15.4 cm−1 , which we tentatively ascribe to β01 . We have considered several possibilities why this fundamental does appear: (1) Existence of several different S0 state forms, as is predicted by the calculations. In this case, the R2PI spectra that originate from the ground state v = 0 levels of the different forms should be separable by UV/UV hole-burning spectroscopy. However, UV/UV holeburning spectra measured when burning at the origin band, shown as Figure S2 (Supplemental Information) did not reveal the presence of two (or more) separable v”= 0 species. (2) Excited-state (mCP)2 is effectively C2 -symmetric. While this would make the β ′ vibration totally symmetric (a), δ ′ then becomes non-totally-symmetric (b), leading to a problem in explaining the appearance of the δ ′ fundamental. (3) Zehnacker and co-workers proposed a loss of symmetry upon electronic excitation which would lead to the appearance of the additional fundamentals. 22 Due to the excitonic coupling, the S1 state adiabatic PES has a double-minimum shape along one or more antisymmetric vibrations. 24 While each of the adiabatic S1 state minima have lower local symmetry (C1 ), the molecular symmetry (MS) group of the coupled S1 /S2 states remains Ci , and the symmetry-restriction rules still apply. The question of the (a)symmetry of the coupled S1 /S2 excited states is discussed in detail


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below. (4) For intermolecular complexes of aromatics with noble-gas atoms, Felker and co-workers have shown that vibronic transitions which are nominally forbidden as fundamentals by rigidmolecule selection rules may nevertheless gain significant intensity if they involve intermolecular vibrations in which the aromatic moiety - which carries the electronic transition-dipole moment (TDM) - librates with sufficiently large amplitude, which renders such transitions vibronically active. 37 In (mCP)2 the out-of-plane intermolecular bending vibration β ′ librationally modulates the electronic TDMs of both monomers, and this may render the β ′ fundamental active in the spectrum. Considering the very small energy differences between the S0 state minima discussed in Section 4, we expect the potential energy surface along the δ and β normal coordinates to be very flat. It is therefore probable that the lowest-frequency vibrations are delocalized over several ground state structures. The δ -mode interconnects the Ci -minima via the C2h -structure, while the β -mode interconnects the two V-shape C2 minima via the C2h -structure. The δ mode is ag in Ci and β is a in C2 symmetry, respectively, but not in C2h . On the other hand, their first overtone is fully allowed in all symmetries. This might explain the intensities of the measured spectrum: Both fundamental transitions are weak, while the corresponding overtones are much more intense.

5 Discussion 5.1 Excitonic Splitting and Isotope Effects Isotopic substitution by even a single 13 C or a D atom breaks the inversion symmetry of (mCP)2 strongly enough to render also the S0 → S2 transition allowed. The 2C-R2PI spectra of both 12 C/13 C-substituted

and H/D-substituted dimers were measured, in order to break the dimer sym-

metry in two ways, allowing to measure two S1 /S2 splittings. Figure 6(a) compares the origin region of all-12 C-(mCP)2 to that of 13 C-(mCP)2 in Figure 6(b). The 13 C-(mCP)2 spectrum shows an additional weak band at 33264 cm−1 , about 8 cm−1 above the intense S0 → S1 000 transition at 13 ACS Paragon Plus Environment


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33256 cm−1 . The former is assigned to the S0 → S2 000 transition, giving the excitonic splitting ∆obs,13C = 8.0 ± 0.4 cm−1 .

12 C/13 C

isotopic contribution: The changes in the zero-point vibrational energy (ZPVE) upon iso-

topic substitution lead to an 12 C/13 C isotopic shift of the 000 transition ∆iso which contributes to the splitting. In the dimers (benzoic acid)2 14 and (benzonitrile)2 , 15 the analogous isotopic shifts were ∆obs13C = 3.3 cm−1 and ∆obs13C = 3.9 cm−1 , respectively. These small shifts may be treated by √ second-order degenerate perturbation theory, as ∆obs13C = ∆2exc + ∆2iso,13C . The ∆iso,13C contribution was determined by measuring the monomer 2C-R2PI spectra of mCP and 13 C-mCP. Figure 7 shows that the S0 → S1 origin of 13 C-mCP is shifted by +3.3 ± 0.4 cm−1 relative to that of mCP. Thus, the purely excitonic contribution ∆exc to the splitting between the S1 and S2 origin bands is √ ∆exc = ∆2obs,13C − ∆2iso,13C = 7.3 ± 0.5 cm−1 . H/D isotope shift: Figure 6(c) shows the origin region of (mCP-h)(mCP-d). The intense S0 → S1 000 transition lies at 33260 cm−1 , here the weaker S0 → S2 000 band appears at 33270 cm−1 . The latter transition is more intense compared to of

13 C-(mCP)

try breaking by H/D exchange as compared to

12 C/13 C

2,

which indicates a stronger symme-

substitution, and also a stronger exciton

localization, see below. The observed S1 /S2 splitting is ∆obs,D = 10 cm−1 , or 2 cm−1 larger than for the 13 C-isotopomer. H/D substitution changes the ZPVE than 12 C/13 C exchange, because the relative change of mass is much larger. The R2PI spectra of (mCP-d)(mCP-h) and (mCP-d)2 are compared to that of (mCP)2 in Figure 8. The R2PI spectrum of non-deuterated (mCP)2 shown in Figure 8(a) shows the same vibronic structure as that of the doubly O-H/O-D deuterated homodimer (mCP-d)2 , Figure 8(c). However, in the (mCP-d)(mCP-h) heterodimer, the inversion symmetry is broken, rendering the R2PI spectrum much more complex as both the S0 → S1 and S0 → S2 transitions are allowed, giving rise to more vibronic bands, see Figure 8(b). The excitonic splitting ∆exc = 7.3 cm−1 determined above allows to extract ∆iso,D = 6.8 cm−1 from the observed √ splitting ∆obs,D as ∆iso,D = ∆2obs,D − ∆2exc = 10 cm−1 as 6.8 cm−1 .


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Vibronic quenching : To relate the observed excitonic splitting of ∆exc = 7.3 cm−1 to the calculated electronic Davydov-splitting ∆el (e.g., 179 cm−1 with the SCS-CC2/aVTZ method), the latter must be reduced or “quenched” by the dimensionless vibronic quenching factor Γvibron , using Förster’s perturbation theory ansatz: 13 ∆vibron = ∆el · Γvibron ,

(11)

The vibronic quenching factor, Γvibron = ∏i exp(−Si ) is the product of the individual vibrational quenching factors γi = exp(−Si ) ≤ 1, where i ranges over all totally-symmetric vibrational modes of the monomer and Si is the i-th dimensionless vibrational displacement between the S0 and S1 state along the vibrational coordinate Qi (Huang-Rhys factor). Si is a measure for the intensity of the corresponding vibronic line and can be obtained (1) experimentally, from the intensities of totally-symmetric vibronic band fundamentals in the dispersed fluorescence spectrum of the mCP 15 (2) computationally from the κ coupling parameters of the monomer monomer, giving Γexp i vibron ; 15 S0 ↔ S1 transition, as described in section 5.2, giving Γcalc vibron ; (3) following a different computaef f

tional path, Γvibron can be calculated via the effective-mode approximation, giving Γvibron . 24 Table 4 lists the mode-specific quenching factors γi of the mCP monomer and the total vibronic calc quenching factors Γexp vibron and Γvibron . After quenching the calculated Davydov splitting ∆el = exp −1 179 cm−1 with Γexp vibron (column 4 of Table 4) one obtains ∆vibron = 7.7 cm , which is in excellent

agreement with the experimentally observed splitting ∆exc = 7.3 cm−1 . When quenching ∆el with calc −1 Γcalc vibron , we obtain ∆vibron = 24.2 cm ; the same value is obtained upon quenching with Γvibron . ef f

The latter two values are more than three times larger than experimentally observed. The reason for this can be seen in columns 2 and 3 of Table 4, which shows that many of the Huang-Rhys factors γi calculated for the S↔ S1 transition of mCP are lower than the experimental ones.



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5.2 Determination of the (mCP)2 Coupling Parameters The coupling constants necessary for the MCTDH simulation were obtained by taking the SCSCC2/aVTZ Ci -symmetric ground state equilibrium geometry as reference geometry in the vibronic coupling formalism and subsequently distorting along every normal mode. The inter- and intrastate coupling constants (λ and κ ) were determined from least squares fits of the analytical expressions for the adiabatic surfaces (Eqs. 5 and 6, omitting ωg/u ) to the ab initio calculated excitation energies. This procedure has been successfully employed for the dimers of 2-pyridone and of orthocyanophenol. 16,18 The coupling parameters for the ag and au normal modes with a frequency up to 600 cm−1 are listed in Tables 5 and 6, respectively. Modes marked by an asterisk are considered in the LVC and QVC simulations. The corresponding normal-mode eigenvectors are shown in Figures 9 and 10. The criterion for including a mode in the LVC and QVC simulations is that its frequency is smaller than 600 cm−1 and that its Huang-Rhys factor is Si > 0.02. Figure 11 shows the fits to the excitation energies along the selected ag modes. The quadratic coupling constant γ is a measure of frequency change: A negative/positive curvature of the excitation energies indicates a frequency lowering/increase upon electronic excitation. 16 For the au vibrations, the coupling constants are calculated from fits to the sum and the difference of the adiabatic potential energy curves along the antisymmetric normal coordinates Qu , shown in Figure 12. The curvature of the difference of the adiabatic PES is a measure of the linear coupling constant

λ : The stronger the curvature, the larger λ .

5.3 Vibronic Spectrum Simulation The simulation of the excited state vibronic spectrum was performed with the MCTDH program package 38 using the linear (LVC) and quadratic (QVC) vibronic coupling models. Both simulations are shown in Figure 13(b) and (c) along the experimental spectrum, Figure 13(a), in the spectral region up to 600 cm−1 . All spectra are set to a common origin. The simulations include seven totally-symmetric (ag ) and five au modes. The corresponding coupling constants are collected in Tables 5 and 6. We account for the higher-frequency modes by introducing a prequenched 16 ACS Paragon Plus Environment

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energy gap of 59.0 cm−1 between the two electronic states, which is determined by treating the high-frequency coupling modes within Förster’s perturbation theory approach. For details on the prequenching, see ref. 18; the prequenching concept has successfully been applied to the dimers of ortho-cyanophenol and 2-pyridone. 16,18 In all cases, the ground state potentials are taken to be harmonic with frequencies ωg/u . The LVC simulation only contains the linear coupling parameters

κ and λ , while the QVC calculation additionally includes the quadratic coupling parameters γ . For mode ν1 we introduce an exception in the QVC simulation. In this case the combination of the harmonic ground state with the quadratic coupling terms would lead to an unphysical behavior of the PES (unbound from below). To stay in line with our model approach we therefore neglect the quadratic coupling terms for mode ν1 . The initial wave function is chosen as a product of harmonic oscillator functions. The line assignments for the LVC and QVC spectra are collected in Table 7 and are based on the nodal structures of the respective vibronic densities. In the LVC simulation shown in Figure 13(b), the calculated frequencies are close to the experimentally observed ones shown in Figure 13(a), especially below 400 cm−1 , see also Table 3. The intensities of the stagger (δ ) and in-plane nitrogen-bend (δ CC-N) are well reproduced. The intensities of the σ transitions are underestimated by the simulation compared to the experiment. The same applies to χ . It may be due to the different ground state structures present that the transitions of σ and χ are larger in the experimental spectrum, as these vibrations are totally-symmetric for all geometries. Also, the band intensities of R2PI spectra are not as reliable as for example the intensities of DF spectra, because they are sensitive to temperature and saturation effects. Nonetheless, the structure of the simulated spectrum shows a similarity to the observed spectrum, although fewer bands could be reproduced, especially in the low-energy region. In the high-energy region, 6a10 shows combinations with δ01 , σ01 and χ01 , which agrees well with experiment. The intensity of 6a10 is overestimated. In general, the frequencies in the spectrum above 400 cm−1 are not well reproduced by the LVC simulation and the intensities are overestimated. The QVC simulation in Figure 13(c) shows intensities closer to experiment in the low-energy region compared to the LVC spectrum, especially for the σ bands. The 6a10 intensity is overes-



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timated, while the intensity of δ CC-N10 and 6b10 are very reasonable. Also, the frequencies have changed markedly. For the higher energy region of the spectrum (≥400 cm−1 ), the frequencies of the QVC simulation are closer to the R2PI spectrum than the LVC frequencies. However, for the low-energy region the opposite is the case: Most frequencies are somewhat too small in the QVC simulation, although the deviation to experiment is reduced compared to the LVC results. While the frequencies for the totally symmetric modes in the calculated spectra well match the harmonic ground state frequencies, for the coupling modes ω , δ C-OHas and 6aas the frequencies for excitation of one quantum are larger in the LVC model than the ground state frequency. In the QVC scheme, this increase is compensated by the negative quadratic coupling constants. Regarding symmetry selection rules, the excitation of odd quanta in the coupling modes should not be observed. However, they appear because, due to the coupling of the electronic S1 and S2 states, the vibronic wave functions have components associated with both electronic states. As demonstrated earlier, this results in non-adiabatic effects and may lead to complicated spectral features. 16,18 The overall shape of the spectrum is reproduced although certain bands of the out-plane vibrations are missing in the simulation because the Huang-Rhys factor is too small. As discussed previously, the use of Cartesian displacement coordinates can be problematic for the low-frequency out-of-plane modes. 16 Table 7 gives an overview over the observed and simulated frequencies for the LVC and QVC model. The extremely small Huang-Rhys factors of out-of-plane modes (see Tables 5 and 6) indicate that the coupling parameters may not be of good quality. The displacement around the equilibrium geometry (Q = 0) is performed along the Cartesian normal-mode eigenvectors of every vibration. Especially at large displacements this may lead to incorrect bond length changes. This problem can be overcome by employing internal coordinates, rather than the Cartesian normal-mode eigenvectors. This has the advantage that no bond length changes are mixed into angular deformations, but is beyond the scope of this work.


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5.4 Localization of the Excitation The localization of the excitation in the different species is determined in the same way as for (benzoic acid)2 and (benzonitrile)2 . 14,15 For both homodimers (mCP-h)2 and (mCP-d)2 , only the S0 → S1 transition is observed, see Figure 8. Therefore, the excitation is fully delocalized over both monomers. Breaking the inversion symmetry leads to a partial localization. 14,15 Degenerate perturbation theory allows to determine the localization of the wave functions by means of the mixing angle α , which is defined as tan(2α ) = |∆exc |/|EA∗ B − EAB∗ |; 19 for details, see refs. 14 and 15. First we consider the

13 C-isotopomer,

where α = 21.1◦ . Therefore, Ψ+ is 86% localized on

monomer A (12 C-mCP) and only 14% on monomer B (13 C-mCP), and vice versa for Ψ− . For (mCP-h)(mCP-d) α = 18.1◦ , leading to Ψ+ being 90% localized on monomer A (mCP-h) and 10% localized on monomer B (mCP-d), and again vice versa for Ψ− . These ratios can be compared ± to experimental observations via the dimer oscillator strengths fdim , see refs. 14 and 15. For 13 C-(mCP)

2,

− + : fdim = 1 : 0.19 results. The integrated intensities of the a calculated ratio of fdim

experimental S0 → S1 and S0 → S2 origins shown in Figure 6 are in good agreement, being 1 : 0.10. This indicates that the determined isotopic and excitonic contributions are reliable. From the − + determined splitting in (mCP-h)(mCP-d), the calculated intensity ratio is fdim : fdim = 1 : 0.26; the

experiment yields 1 : 0.30, in excellent agreement. Consequently, the

13 C-substitution

leads to a

smaller localization of the excitation compared to partial deuteration of mCP. Nevertheless, in both heterodimers the monomers are distinguishable in the excited state. The excitation can oscillate back and forth between the monomers upon excitation with a large enough bandwidth to cover both origins. 19 For the homodimers (mCP)2 and (mCP-d)2 the angle is α = π /4; the semiclassical exciton transfer rate is kAB = 4|VAB |/h = 2|∆exc | · c, 19 resulting in a transfer rate of kAB = 4.4 · 1011 s−1 , which is equivalent to an exciton hopping time of texc = (kAB )−1 = 2.3 ps. This is much faster compared to the benzoic acid dimer (17.7 ps) 14 and the benzonitrile dimer (8.0 ps). 15 A possible reason is the much smaller intermolecular distance: RAB = 5.34 Å for (mCP)2 , while in (BZA)2 19 ACS Paragon Plus Environment


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and (BN)2 the monomers are 7.14 Å and 6.53 Å apart, respectively. 14 For the heterodimers, the excitation is partially localized, therefore the transfer rate should decrease and the hopping time increase compared to the electronically delocalized homodimers. The transfer rate of 13 C-(mCP)2 is determined to be kAB = 1.6 · 1011 s−1 , corresponding to texc = 6.3 ps. The increase in hopping time is very small compared to (mCP)2 , agreeing with a partial localization. For (mCP-h)(mCP-d), the transfer rate is kAB = 7.1 · 1010 s−1 . The decrease in kAB is a bit larger compared to the 13 C-(mCP)2 . The hopping time is therefore a little longer, texc = 14 ps. Thus, the excitation is slightly more localized in (mCP-h)(mCP-d) compared to 13 C-(mCP)2 .

5.5 Asymmetry of the First Excited State Due to the appearance of the out-of-plane fundamental β01 , Seurre et al. suggested a symmetry loss upon excitation breaking the inversion center. 22 Based on this they concluded a localization of the excitation on the monomers. The S1 state geometry optimization of (mCP)2 shows indeed an asymmetric deformation. Both rings expand upon excitation, but the C-C bond lengths in monomer A increase by 28 − 54 pm, while they increase only by 12 − 14 pm in monomer B. This leads to a C1 symmetry. Table 8 details the bond lengths and structure parameters of the S0 and S1 states. For symmetry reasons, there is a second dimer structure, in which the deformations on A and B are exchanged. This structure corresponds to the symmetry-equivalent and degenerate minimum of the double-well type S1 adiabatic potential of (mCP)2 . Both the S1 and S2 states of the dimer are delocalized over both minima, therefore, the geometry change does not imply localization of the excitation in an asymmetric structure. This is illustrated by the adiabatic PESs of the first and ef f

second excited state along the antisymmetric effective mode coordinate Q− in Figure 14. The aspect of localization in case of isotopic substitution is treated above in detail.


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6 Conclusions The S1 /S2 excitonic splitting of the Ci -symmetric dimer (meta-cyanophenol)2 is not directly measurable by optical spectroscopy, because its S0 → S1 (Ag → Au ) transition is electric-dipole allowed, while the S0 → S2 (Ag → Ag ) transition is dipole-forbidden. A single 12 C/13 C or H/D substitution breaks the inversion symmetry of (mCP)2 sufficiently to render the S0 → S2 transition somewhat allowed. We have measured mass-selected two-color resonant two-photon ionization spectra of the S0 → S1 and S0 → S2 electronic origins of bining the information of the

13 C-(mCP)

2

12 C/13 C

or H/D substituted dimers of mCP. Com-

and (mCP-h)(mCP-d) heterodimer spectra allows to

experimentally determine the excitonic splitting of (mCP)2 as ∆exc = 7.3 cm−1 . CC2 and SCS-CC2 calculations predict three close-lying ground-state structures of (mCP)2 : The lowest is near-planar but slightly Z-shaped (Ci -symmetric, two enantiomers), the secondlowest structure is 0 − 5 cm−1 higher and is planar and C2h -symmetric. The third structure is 3 − 11 cm−1 higher and is V-shaped (C2 -symmetric, two enantiomers). CC2 and SCS-CC2/aVDZ calculations predict a π -stacked dimer geometry, which is 270 − 470 cm−1 higher; this structure is not a minimum at the SCS-CC2/aVTZ level. The isotope-dependent shifts in the S0 → S1 /S2 origin bands of the

13 C-(mCP)

2

and (mCP-

h)(mCP-d) heterodimers arise from the changes of the vibrational zero-point energy between the electronic ground and excited states. The isotope shift that arises from a single 12 C/13 C substitution was determined as ∆iso,13C = 3.3 cm−1 ; we do not observe any dependence on the position of the 13 C atom within the dimer, although there must be small effects.

The isotope effect that arises from

H/D exchange in the phenolic OH group is somewhat larger, being ∆iso,D = 6.8 cm−1 . This leads to a larger splitting between the vibrationless levels of the S1 and S2 states. The purely electronic (vertical) excitonic splitting calculated with the SCS-CC2 method and the aug-cc-pVTZ basis set is ∆el = 179 cm−1 . The large difference between this value and the experimental ∆exc = 7.3 cm−1 reflects the importance of vibronic coupling, which reduces or quenches the purely electronic splitting. The vibronic quenching factor Γvibron = Πi γi that is experimentally determined from the mCP dispersed fluorescence spectrum, Γexp vibron = 0.043, yields 21 ACS Paragon Plus Environment


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exp −1 ∆exp vibron = ∆el · Γvibron = 7.7 cm , in very good agreement with the experiment. The quenching

factor Γcalc vibron derived from the mCP monomer calculated S0 → S1 spectrum is three times larger, −1 resulting in a ∆calc vibron = 24.2 cm .

Our conclusion that the excitonic excitations are delocalized is in disagreement with the interpretation of Seurre et al., 22 but not with their experimental observations. The excitonic coupling between S1 and S2 gives rise to two asymmetric S1 state minimum-energy geometries, corresponding to a potential with two symmetry-equivalent minima along the antisymmetric effective mode ef f

coordinate Q− . While the rigid-molecule symmetry at these minima is reduced from Ci to C1 , the molecular symmetry (MS) group of the S1 state including tunneling remains Ci (M). 15–18 We interpret the appearance of the fundamental of the low-frequency out-of-plane mode β ′ in the S0 → S1 spectra as deriving from the strongly librational character of the β vibration, which modulates the electronic TDM strongly enough to induce the appearance of fundamental transitions in this nominally antisymmetric mode by a Herzberg-Teller-like mechanism. 37 The simulation of the vibronic spectrum with MCTDH agrees fundamentally with the structure of the in-plane modes observed experimentally. Issues arose for the description of out-of-plane modes, as the predicted Huang-Rhys parameters were far too small to cause these modes to appear in the spectrum. Apparently, the geometry displacement along the normal-mode eigenvectors is not the best description and internal coordinates would be necessary for a complete description and simulation of the out-of-plane modes. Nevertheless, the simulations agrees with the observed spectrum and differences of linear and quadratic vibronic coupling have been illustrated.

Acknowledgments This work was supported by the Schweiz. Nationalfonds (project nos. 200020-152816 and 132540) and the Deutsche Forschungsgemeinschaft (project no. AZ KO945/17-1).

Supporting Information Available: Figure S1 with the C2 -symmetric, stacked structure of the meta-cyanophenol dimer (not observed experimentally). Figure S2 with UV/UV-holeburned spec-


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trum, Tables S1 to S4 with Cartesian coordinates of the SCS-CC2/aug-cc-pVTZ optimized four structures in Table 1.

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(9) Müller, A.; Talbot, F.; Leutwyler, S. S1 /S2 Exciton Splitting in the (2-Pyridone)2 Dimer. J. Chem. Phys. 2002, 116, 2836–2847. (10) Ottiger, P.; Leutwyler, S.; Köppel, H. S1 /S2 Excitonic Splittings and Vibronic Couplings in the Excited-State of the Jet-Cooled 2-Aminopyridine Dimer. J. Chem. Phys. 2009, 131, 204308–1–11. (11) Ottiger, P.; Leutwyler, S. Excitonic Splittings in Jet-Cooled Molecular Dimers. CHIMIA 2011, 65, 228–230. (12) Heid, C. G.; Ottiger, P.; Leist, R.; Leutwyler, S. The S1 /S2 Exciton Interaction in 2-Pyridone·6-Methyl-2-Pyridone: Davydov Splitting, Vibronic Coupling and Vibronic Quenching Effects. J. Chem. Phys. 2011, 135, 154311–1–15. (13) Ottiger, P.; Leutwyler, S.; Köppel, H. Vibrational Quenching of Excitonic Splittings in HBonded Molecular Dimers: The Electronic Davydov Splittings Cannot Match Experiment. J. Chem. Phys. 2012, 136, 174308–1–13. (14) Ottiger, P.; Leutwyler, S. Excitonic Splitting and Coherent Electronic Energy Transfer in the Gas-Phase Benzoic Acid Dimer. J. Chem. Phys. 2012, 137, 204303. (15) Balmer, F. A.; Ottiger, P.; Leutwyler, S. Excitonic Splitting, Delocalization, and Vibronic Quenching in the Benzonitrile Dimer. J. Phys. Chem. A 2014, 118, 11253–11261. (16) Kopec, S.; Ottiger, P.; Leutwyler, S.; Köppel, H. Analysis of the S2 ← S0 Vibronic Spectrum of the ortho-Cyanophenol Dimer Using a Multimode Vibronic Coupling Approach. J. Chem. Phys. 2015, 142, 084308–1–16. (17) Ottiger, P.; Köppel, H.; Leutwyler, S. Excitonic Splittings in Molecular Dimers: Why Static Ab Initio Calculations Cannot Match Them. Chem. Sci 2015, 6, 6059–6068. (18) Kopec, S.; Köppel, H. Theoretical Analysis of the S0 → S2 Vibronic Spectrum of the 2Pyridone Dimer. J. Chem. Phys. 2016, 144, 024314–1–13. 24 ACS Paragon Plus Environment

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(19) Förster, T. In Modern Quantum Chemistry; Sinanoglu, O., Ed.; Academic Press, New York, 1965; Chapter III. B, p 93. (20) Fulton, R. L.; Gouterman, M. Vibronic Coupling. I. Mathematical Treatment for Two Electronic States. J. Chem. Phys. 1961, 35, 1059–1071. (21) Fulton, R. L.; Gouterman, M. Vibronic Coupling. II. Spectra of Dimers. J. Chem. Phys. 1964, 41, 2280–2286. (22) Seurre, N.; Barbu-Debus, K. L.; Lahmani, F.; Zehnacker-Rentien, A.; Sepiol, J. Electronic and Vibrational Spectroscopy of Jet-Cooled m-Cyanophenol and its Dimer: Laser-Induced Fluorescence and Fluorescence-Dip IR Spectra in the S0 and S1 states. Chem. Phys. 2003, 295, 21–33. (23) Köppel, H.; Domke, W.; Cederbaum, L. S. Multimode Molecular Dynamics Beyond the Born-Oppenheimer Approximation. Adv. Chem. Phys. 1984, 57, 59–245. (24) Kopec, S.; Ottiger, P.; Leutwyler, S.; Köppel, H. Vibrational Quenching of Excitonic Splittings in H-Bonded Molecular Dimers: Adiabatic Description and Effective Mode Approximation. J. Chem. Phys. 2012, 137, 184312–1–10. (25) Nebgen, B.; Emmert, F. L.; Slipchenko, L. V. Vibronic Coupling in Asymmetric Bichromophores: Theory and Application to Diphenylmethane. J. Chem. Phys. 2012, 137, 084112– 1–12. (26) Nebgen, B.; Slipchenko, L. V. Vibronic Coupling in Asymmetric Bichromophores: Theory and Application to Diphenylmethane-d5. J. Chem. Phys. 2014, 141, 134119–1–9. (27) Pillsbury, N. R.; Kidwell, N. M.; Nebgen, B.; Slipchenko, L. V.; Douglass, K. O.; Cable, J. R.; Plusquellic, D. F.; Zwier, T. S. Vibronic Coupling in Asymmetric Bichromophores: Experimental Investigation of Diphenylmethane-d5 . J.Chem. Phys. 2014, 141, 064316–1–9.



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(28) Meyer, H.-D.; Manthe, U.; Cederbaum, L. S. The Multi-Configurational Time-Dependent Hartree Approach. Chem. Phys. Lett. 1990, 165, 73–78. (29) Meyer, H.-D.; Gatti, F.; Worth, G. A. Multidimensional Quantum Dynamics: MCTDH Theory and Application; Wiley-VCH, 2009. (30) Beck, M. H.; Jäckle, A.; Worth, G. A.; Meyer, H.-D. The Multiconfigurational TimeDependent Hartree (MCTDH) Method: A Highly Efficient Algorithm For Propagating Wavepackets. Phys. Rep. 2000, 324, 1–105. (31) Hättig, C.; Weigend, F. CC2 Excitation Energy Calculations on Large Molecules using the Resolution of the Identity Approximation. J. Chem. Phys. 2000, 113, 5154–5161. (32) Hättig, C. Geometry Optimizations with the Coupled-Cluster Model CC2 using the Resolution of the Identity Approximation. J. Chem. Phys. 2003, 118, 7751–7761. (33) Hellweg, A.; Grün, S. A.; Hättig, C. Benchmarking the Performance of Spin-component Scaled CC2 in Ground and Electronically Excited States. Phys. Chem. Chem. Phys. 2008, 10, 4119–4127. (34) Winter, N.; Graf, N. K.; Leutwyler, S.; Hättig, C. Benchmarks for 0-0 Transitions of Aromatic Organic Molecules: DFT/B3LYP, ADC(2), CC2, SOS-CC2 and SCS-CC2 Compared to High-Resolution Gas-Phase Data. Phys. Chem. Chem. Phys. 2013, 15, 6623–6630. (35) TURBOMOLE V6.3 2011;

a development of Universität Karlsruhe (TH) and

Forschungszentrum Karlsruhe GmbH, 1989-2007, TURBOMOLE GmbH; available from http://www.turbomole.com. (36) The thresholds for SCF and one-electron density convergence were set to 10−9 a.u. and 10−8 a.u., respectively. The convergence thresholds for all structure optimizations were set to 10−8 a.u. for the energy change, 6 · 10−6 a.u. for the maximum displacement element,


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10−6 a.u. for the maximum gradient element, 4 · 10−6 a.u. for the RMS displacement and 10−6 a.u. for the RMS gradient. (37) Maxton, P. M.; Schaeffer, M. W.; Ohline, S. M.; Kim, W.; Venturo, V.; Felker, P. M. The Raman and Vibronic Activity of Intermolecular Vibrations in Aromatic-Containing Complexes and Clusters. J. Chem. Phys. 1994, 101, 8391–8408. (38) Worth, G. A.; Beck, M. H.; Jäckle, A.; Meyer, H.-D. The MCTDH Package, Version 8.4. 2007; University of Heidelberg, Heidelberg, Germany. http://mctdh.uni-hd.de.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Table 1: Calculated Relative Energies (in cm−1 ) of the Four Lowest-Energy (m-Cyanophenol)2 Structures, see Figure 2.

CC2/aug-cc-pVDZ CC2/aug-cc-pVTZ SCS-CC2/aug-cc-pVDZ SCS-CC2/aug-cc-pVTZ a b

Z-shaped Planar Ci C2h 0.0 0.0 0.0 5.5b 0.0 0.0 0.0 0.1

V-shaped π -Stacked a C2 C2 11.3 474.4 7.5 315.9 11.4 272.6 3.1 –

shown in Figure S1 (Supplemental Information). index-1 saddle point


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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 2: Calculated Vertical Excitation Energies and Davydov-splitting Energies ∆el (in cm−1 ) of the H-bonded (m-Cyanophenol)2 Structures, see Figure 2.

Z-shaped (Ci ) Irred. S1 Au S2 Ag ∆el Planar (C2h ) S1 Bu S2 Ag ∆el V-shaped (C2 ) S1 B S2 A ∆el

CC2/aVDZ Eexc fel 35369 0.157 35563 0.000 194

CC2/aVTZ Eexc fel 35849 0.160 36045 0.000 196

SCS-CC2/aVDZ Eexc fel 35412 0.123 35585 0.000 173

SCS-CC2/aVTZ Eexc fel 35935 0.134 36114 0.000 179

35369 35562 193

0.157 0.000

35845 36046 201

0.160 0.000

35411 35585 174

35935 36115 180

35370 35562 194

0.157 4 · 10−4

35187 35379 192

0.152 4 · 10−4

35412 35585 173


0.123 0.000

0.123 35936 −4 3 · 10 3E-04 36115 179

0.134 0.000

0.134 3 · 10−4


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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Table 3: Experimental S0 and S1 Frequencies (in cm−1 ) of (m-Cyanophenol)2 and SCS-CC2/augcc-pVTZ S0 Frequencies and Comparison to Assignments of Ref. 22. Vibration S1 δ01 β01 δ02 β02 β04 θ02 σ01 σ01 δ01 θ02 δ02 σ01 δ02 χ01 χ01 δ01 σ02 δ CC-N10 σ02 δ01 σ02 δ02 χ02 σ03 σ03 δ01 σ03 δ02 δ C-OH10 δ C-OH10 δ01 6a10 6a10 δ01 6a10 β01 6a10 δ02 δ C-OH10 σ01 6b10 6a10 σ01 δ C-CN10 6a10 χ01 6a10 σ02 6b10 σ01

2C-R2PI Ref. 22(S1 ) 12.8 30 15.4 12 27.3 30.4 60.8 70.6 84.5 75 97.3 99.3 111.2 116.9 84 127.6 167.1 176.7 180.0 193.8 225.8 248.4 263.4 275.0 394.9 407.6 413.5 425.0 430.8 439.4 478.5 496.6 498.8 523.5 529.8 578.0 582.6

Vibration S0 δ10 β10 β20 σ10 χ10 δ10 χ10 σ20 δ CC-N01

Fluorescence SCS-CC2/aVTZ 15 11 (17.5)a 13 35 75 79 103 109 119 148 168 171

Frequency from the first overtone.


Ref. 22(S0 ) 34 11 104 75

165

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Table 4: SCS-CC2/cc-pVTZ calculated and experimental frequencies (in cm−1 ) of the totallysymmetric vibrations of m-cyanophenol, calculated and experimental mode-specific quenching exp factors γi = exp(−Si ), calculated and experimental total quenching factors Γcalc vibron and Γvibron . SCS-CC2/cc-pVTZ Frequency/cm−1 γi,calc a 141.8 0.975 387.4 0.991 450.9 0.652 527.7 0.817 558.2 0.975 720.7 0.887 942.5 0.942 1003.9 0.660 1093.8 0.977 1167.4 0.924 1180.0 0.993 1195.5 0.995 1299.4 0.856 1339.4 0.931 1436.2 0.993 1466.0 0.950 1517.8 0.997 1629.7 0.999 1634.1 0.988 2106.2 0.904 3201.2 0.950 3214.6 0.989 3231.3 0.993 3239.9 0.982 3793.4 0.893 Γcalc 0.135 calc ∆vibron 24.2 cm−1 a b

Experimental Freq. / cm−1 γi,exp b 146.5 0.942 453.2 531.2 564.1 718.0 935.7 1004.4 993.7

0.439 0.637 0.960 0.867 0.842 0.446 0.900

1286.5

0.591

Γexp ∆calc vibron

0.0434 7.7 cm−1

from calculated coupling constants of mCP. from fluorescence band intensities of mCP.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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Table 5: Vibronic coupling parameters (in cm−1 ) based on SCS-CC2/aVTZ excited state potential fits for totally symmetric ag modes. The mode number corresponds to the Turbomole numbering, for spectral reference the Wilson nomenclature is given in parenthesis. ωg is the calculated frequency, κ the intrastate coupling constant, γ the quadratic coupling parameter and Si the HuangRhys factor. ag -Mode 1* (δ )

ωg 10.8

State S1 S2 4* (σ ) 79.2 S1 S2 6* (χ ) 108.5 S1 S2 7 139.2 S1 S2 9* (δ CC-N) 171.4 S1 S2 11 221.7 S1 S2 13 381.1 S1 S2 16 (δ C-OH) 412.7 S1 S2 18* (6a) 458.2 S1 S2 19 460.5 S1 S2 21* (6b) 528.4 S1 S2 23* (δ C-CN) 569.4 S1 S2

κ −4.8 1.0 55.1 49.6 −30.3 −27.3 −4.5 −4.7 79.9 73.5 −3.5 −3.9 2.7 3.4 −21.7 −27.3 321.1 319.7 36.1 36.0 229.1 208.8 −136.3 −132.3

γ −459.4 −463.0 −9.7 −9.9 −14.5 −14.3 −63.2 −63.2 −43.8 −43.1 −42.4 −44.9 −168.5 −168.7 −2.6 −3.5 −34.5 −35.7 −66.8 −70.6 −34.4 −35.7 −0.3 −1.3


Si 0.100 0.004 0.242 0.196 0.039 0.032 0.001 0.001 0.109 0.092 1.2E-04 1.6E-04 2.5E-05 3.9E-05 0.001 0.002 0.246 0.243 0.003 0.003 0.094 0.078 0.029 0.027

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Table 6: Vibronic coupling parameters (in cm−1 ) based on SCS-CC2/aVTZ excited state potential fits for non-totally symmetric modes of au symmetry. The mode number corresponds to the Turbomole numbering, for spectral reference the Wilson nomenclature is given in parenthesis. ωu is the calculated frequency, λ the interstate coupling constant, γ the quadratic coupling parameter and Si the Huang-Rhys factor. au -Mode 2 (β ) 3 (θ ) 5* (ω ) 8 10 (δ CC-Nas ) 12 14 15* (δ C-OHas ) 17* (6aas ) 20 22* (6bas ) 24* (δ C-CNas )

ωu 13.0 47.2 99.5 143.6 183.8 224.2 382.3 412.1 458.2 465.3 528.5 571.8

λ γ1 γ2 Si 0.03 −377.0 −373.6 1.9E-06 0.05 −21.7 −23.4 5.2E-07 35.4 −52.6 −38.2 0.063 0.6 −61.4 −61.4 7.6E-06 12.0 −30.2 −30.3 0.002 0.1 −44.2 −45.1 9.5E-08 8.3 −170.0 −170.0 2.4E-04 117.9 −7.4 −2.3 0.041 298.0 −33.9 −33.8 0.212 2.1 −69.0 −71.9 1.0E-05 204.5 −35.1 −35.2 0.075 113.9 −3.7 6.8 0.020



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Table 7: Vibrational frequencies (in cm−1 ) in the experimental 2C-R2PI spectrum and in the linear (LVC) and quadratic (QVC) MCTDH simulations. Vibration δ01 σ01 σ01 δ01 χ01 ω01 σ02 δ CC-N10 σ01 χ01 σ01 ω01 σ01 δ CC-N10 χ01 δ CC-N10 ω01 δ CC-N10 δ C-OHas 6a10 6a10 δ01 (6aas )10 6b10 6a10 σ01 δ C-CN10

2C-R2PI 12.8 84.5 97.3 116.9 167.1 176.7

413.5 425.0 496.6 498.5 523.5

LVC 10.8 79.2 90.0 108.5 128.9 158.5 171.4 187.8 208.0 250.6 279.9 442.3 458.5 469.4 479.0 528.4 537.8 569.6

QVC 10.7 74.2 85.0 101.0 93.3 148.3 148.0 175.2 167.5 222.1 249.1 241.4 435.3 440.8 451.5 457.8 511.1 514.9 569.4


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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 8: Characteristic structure parameters (in Å) of (meta-cyanophenol)2 in the SCS-CC2/aVTZ optimized S0 and S1 states. N’ stands for the N atom of B. S0 (Ci ) A=B r(C1 -C2 ) 1.397 r(C2 -C3 ) 1.403 r(C3 -C4 ) 1.394 r(C4 -C5 ) 1.398 r(C4 -C5 ) 1.399 r(C5 -C6 ) 1.402 r(C6 -C7 ) 1.437 r(C7 -N8 ) 1.176 r(C9 -O10 ) 1.356 r(O10 -H11 ) 0.976 δ (C6 -C7 -N8 ) 174.7◦ δ (C9 -O10 -H11 ) 110.2◦ r(H11 · · · N’8 ) 2.025 r(H11 · · · N’8 ) 2.025 RCOM 5.340 ∆z 0.006 Parameter

S1 (C1 ) A B 1.443 1.410 1.435 1.416 1.431 1.407 1.426 1.410 1.453 1.412 1.446 1.416 1.419 1.449 1.200 1.190 1.349 1.365 0.991 0.982 173.2◦ 174.6◦ 110.8◦ 110.2◦ 1.978 1.914 5.341 0.004



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

RAB θ

Figure 1: SCS-CC2/aug-cc-pVTZ structure and electronic transition dipole moment (TDM) directions of (meta-cyanophenol)2 . The distance between the centers of mass is RAB = 5.34 Å, the angle between the intermonomer distance vector and the TDMs is θ = 11◦ .


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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


a) Z-shaped (Ci)

δ

b) Planar (C2h)

β

c) V-Shaped (C2)

z x

• y

Figure 2: SCS-CC2/aug-cc-pVTZ optimized isomers of (meta-cyanophenol)2 . Left: side views, right: top views. The intermolecular vibrations δ and β interconvert the Ci , C2h and C2 structures.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 38 of 50

θ > 54.7°

a)

S2

+

+ θ

S1

-

-

S2(Bu): repulsive

X

+

θ

S0

b)

+

-

(BN)2, (oCP)2, (2PY)2, (BZA)2, (2PY)2

S1(Ag): attractive

θ < 54.7° S2

+ S1

θ

-

+

S2(Ag): repulsive

X +

+ θ

-

-

S0 S1(Bu): attractive

(mCP)2

Figure 3: Electric-dipole allowed and forbidden S0 → S1 /S2 transitions (left) and corresponding transition dipole-moment vector directions in excitonic homodimers. (a) For θ > 54.7◦ , (b) for θ < 54.7◦ . Full and dashed vertical arrows symbolize allowed and forbidden electronic transitions. Examples of spectroscopically investigated homodimers are given for both cases, see the text.


Page 39 of 50

000

1

Intensity / arb. units

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


σ0n

δCC-N 01 σ01β 02

δ01β02

χ01δ01 χ01β02 δ 01

-25

2

0

χ

β 02

25

50

75

0 1

100

125

150

175

200

225

250

275

300

-1

Relative Wavenumber / cm

Figure 4: Dispersed fluorescence spectrum of (m-cyanophenol)2 with band assignments. The wavenumber scale is relative to the 000 band at 33255 cm−1 .



3

σ n0

1

δ β10

0

2

θ10

σ20 δ10

χ10

β40 θ0

50

2 0

2 0

150

200

1 1

6a0σ0

1 1

νC-CN10

1 2

Intensity x3.9

σ30 δ10

σδ

100

6b0

δC-OH0σ0

1 1 1 1

δC-OH0δ 0

σ10 δ10 θ20δ 20

θ 10δ 10 1 0

1

6a0δ 0

1

δCC-N 0

σ10 δ10

6a0δ 0

δ

2 0

1 2 6a0β 0

6a0 1

δC-OH0

1 2

β 20

6a0σ0 6b10σ10

2

1 1

1

6a0χ 0

000(S1)

Intenstiy / arb. units

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 40 of 50

χ20

σ30 δ20

300 400 250 350 Relative Wavenumber / cm-1

450

500

550

600

Figure 5: Two-color resonant two-photon ionization spectrum of (meta-cyanophenol)2 with assigned vibronic transitions. The scale is relative to the 000 band at 33255 cm−1 .


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Ion Signal / arb. units

Page 41 of 50

000(S1) 33255

a) (mCP)2

0 00(S1) 33256

b) 13C-(mCP)2 0

00(S2)

∆obs = 8 cm-1 000(S1) 33260

c) (mCP-h)(mCP-d) 0

00(S2)

∆obs = 10 cm-1 -10

0 10 15 20 -5 5 Relative Wavenumber / cm-1

25

Figure 6: 2C-R2PI spectra of (a) (meta-cyanophenol)2 , (b) 13 C-substituted and c) H/D substituted heterodimers in the 000 band region. The scale is relative to the 000 band of (mCP)2 at 33255 cm−1 . The 000 band of 13 C-(mCP)2 is at 33256 cm−1 , that of (mCP-h)(mCP-d) at 33260 cm−1 .



000(trans)

a) meta-cyanophenol 0

00(cis)


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 42 of 50

mCP-d / mCP-13C

b)

mCP-d

mCP-d

mCP-13C mCP-13C Intensity x5.6

-6.7 +3.3

34340

34360

-6.7 +3.3

34380 34400 34420 Wavenumber / cm-1

34440

Figure 7: 2C-R2PI spectra of the 000 band region of cis- and trans-meta-cyanophenol. (a) mCP mass channel (m/e=119), b) mCP+1 mass channel (m/e=120) showing the signals of 13 C-mCP and mCP-d.


Page 43 of 50

0

S1(00 ) 33’255

a) (mCP)2

0

S1(00 ) b) (mCP-d)(mCP-h)

0

33’270

S2(00 ) 33’260


0

S1(00 ) c) (mCP-d)2

33’268

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


33250

33300

33400 33350 Wavenumber / cm-1

33450

33500

Figure 8: 2C-R2PI spectra of (a) all-h-(m-cyanophenol)2 , (b) (m-cyanophenol-h)(m-cyanophenold) and (c) (m-cyanophenol-d)2 .



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ν2 (β): 13.0 cm-1

ν15 (δC-OHas): 412.1 cm-1

ν17 (6aas): 458.2 cm-1

ν22 (6bas): 528.5 cm-1

ν24 (δC-CNas): 571.8 cm-1

Figure 9: SCS-CC2/aVTZ calculated eigenvectors of the low-frequency antisymmetric (au ) modes of (m-cyanophenol)2 .


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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


-1

-1

ν1 (δ): 10.8 cm

ν4 (σ): 79.2 cm

ν6 (χ): 108.5 cm-1

ν9 (δCC-N): 171.4 cm-1

ν18 (6a): 458.2 cm-1

ν21 (6b): 528.4 cm-1

ν23 (δC-CN): 569.4 cm-1

Figure 10: SCS-CC2/aVTZ calculated eigenvectors of the low-frequency totally-symmetric (ag ) modes of (m-cyanophenol)2 .



Energy [cm -1]

36000

36250

ν1 S2

35500 S1

35000

ν4

36150 Energy [cm -1]

36500

34500

S2

36050 35950 35850

34000

S1

35750 33500 -3

-2

-1

0

1

2

3

-3

-2

-1

0 Q4

Q1

36100

1

2

3

ν9 S2

Energy [cm -1]

Energy [cm -1]

ν6

S2

36100 36000

S1

35900 35800

35900 35700

S1

35500

-3

-2

-1

0 Q6

1

2

3

-3

37000

ν18

36400

-2

-1

0 Q9

1

2

3

-1

0 Q21

1

2

3

ν21

36000

Energy [cm -1]

36500 Energy [cm -1]

S2

35500 S1

35000 34500 -3

36000

S2

35600 S1

35200 -2

-1

0 Q 18

1

2

-3

3

-2

36600

-1

ν23

S2

36400 Energy [cm ]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 46 of 50

36200 S1

36000 35800 35600 -3

-2

-1

0 Q23

1

2

3

Figure 11: Least-squares fits to the calculated S1 and S2 excitation energies of (m-cyanophenol)2 along the normal-modes Qi of the modes ν1 , ν4 , ν6 , ν9 , ν18 , ν21 and ν23 . The corresponding vibrational eigenvectors are shown in Figs. 10 and fig:vibs-au. The ab initio energies are shown as dots for S1 and crosses for S2 .


Page 47 of 50

ν5

0

Energy [cm ]

Energy [cm -1]

ν15

0

Sum -1

-100 -200 Difference -300

Sum -200 -400 Difference -600

-400 -3

-2

-1

0 Q5

1

2

-800 -3

3

0 ν17 Sum

-800 Difference

-1200

-1

0 Q15

1

2

3

1

2

3

Sum

-1

-400

-400 Difference

-800

-1200

-1600 -3

-2

ν22

0 Energy [cm ]

Energy [cm -1]

-2

-1

0 Q17

1

2

ν24

Sum

0 -1

Energy [cm ]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


3

-3

-2

-1

1

2

3

0 Q22

-200 -400

Difference

-600 -800 -3

-2

-1

0 Q24

Figure 12: Least-squares fits to the sum (dashed) and difference (dotted) of the excitation energies along the normal-mode eigenvectors of the vibrations ν5 , ν15 , ν17 and ν24 . The ab initio energies are shown as dots for S1 and crosses for S2 .



1

σ0

a) experimental 2C-R2PI

1

δ0

Signal / arb. units

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 48 of 50

χ 10

1

δCC-N10

6a0

1

6b0

δC-CN10

δC-OH10

b) linear vibronic coupling 1

1

δ

1 0

ω 10

σ0 χ 10

6a0 δCC-N10

ω 10 σ 1

δ0

0

1 0

(δC-OHas)10

100

δC-CN10

c) quadratic vibronic coupling 1

χ 10

1

6b0

(6aas)10

6a0 1 (δC-OHas) 1 (6aas)0

δCC-N10

1

6b0

0

200 300 400 Relative Wavenumber / cm-1

500

δC-CN10

600

Figure 13: (a) Experimental 2C-R2PI spectrum of (mCP)2 compared to the MCTDH simulated spectra based on (b) the LVC and (c) the QVC model.


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3000 Vad(S1)

2000 Energy / cm-1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Vad(S2)

1000

0

∆vibron = 24 cm-1

∆vert = 179 cm-1

-1000 -4

-2

0 Qeff -

2

4

Figure 14: S1 and S2 excited-state adiabatic potential energy surfaces along the effective mode ef f ef f Q− . The vertical excitation energy splitting ∆vert at the ground state equilibrium geometry Q− = 0 is identical to the calculated Davydov splitting ∆el .



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

13

0 00(S1)

C-(mCP)2

0

00(S2) Δobs = 8 cm-1 33245

33255

33265 cm-1

Figure 15: TOC graphic


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Excitonic Splitting and Vibronic Coupling Analysis of the m

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